Before commiting to the substantial sums of money required for the rebuilds needed to actually use the Southern Rail access project, how about testing if southern access is really attractive by building an urban ropeway conection from Heathrow TErminal 4 to Ashford (Surrey) station?
Theres a route over the reservoirs that doesn't overfly any residential properties with only a single angle tower. The journey time would be a small number of minutes.
Obviously you'd have to run a couple more trains via Ashford to utilise it, but naively I'd suggest it would still be cheaper than the major construction the southern access people are proposing.
Thing is, the Southern Approach to Heathrow would be far, far more useful than such a rope way.
For example in a post HS2 world Woking would be about +1 hour from any HS2 station than Euston by changing at Old Oak Common.
For example Birmingham in about 1:50 (with a circa 20 minute change at Old Oak Common) rather than fastest current journey time of 2:34 (which allows 50 minutes to get across London, which should be possible in 20 minutes). However, the big difference isn't necessarily the time saving, but rather the fact that it's a single change rather than getting from the main platforms at Waterloo to the Northern Line and then from the Northern Line to the main platforms at Euston
Likewise, the extra frequency of services between Guildford/Woking as well as Basingstoke/Farnborough and Farnborough/Woking (less so Basingstoke/Woking due to the fairly high frequency or already sees) would make rail travel much more attractive.
I've previously also suggested (given the limited time saving by running the trains semi fast from Basingstoke and that those wanting to save time would most likely be able to get a fat service and change at Woking, especially those not starting at Basingstoke) if the service was an all stations service beyond Woking you'd attract a lot of local rail travel.
You could potentially solve some of the junction issue at Basingstoke by (rather than a grade separated junction there) extending both the Heathrow and Basingstoke Stoppers services to Oakley (new station on the West of England Line) with a small amount of electrification or batteries.
The current Basingstoke Stoppers would probably need to cross to the London bound platform at Oakley to ensure that they were out of the way of the following WofE Line service (about 8 minutes later) and the return (some times) would have to be squeezed between the WofE Line service and the XC at Basingstoke (which may involve being held at a signal and/or the stopper running from platform 3 whilst the faster train running from platform 4).
The Heathrow services would likely be an easier fit in comparison.
Also, you need to consider the third runway is taking about +50% more flights, there's almost no way you could run that many extra flights and be reliant on road travel to get them to the airport.
The other thing to consider is the motorways are congested now, they almost certainly couldn't cope with the extra traffic from a third runway.
As such it's not just a case of could a rail link be viable now, but what would that look like if it was taking 10% of current vehicles (due to the uplift from the extra runway, which could be as much as +33%)?
10% extra would be the equivalent of about 120 flights a day, of we assume an average of 160 people per flight (based on the most used aircraft which is the A320) that works out at an average of 500 people per hour per direction over an 18 hour day.
Over a 4tph that's 125 people per train, yes that's fairly lightly loaded train, but that's assuming 90% of new passengers travel by other modes and 100% of existing passengers carry on travelling how they currently do. It also assumes no other travel (those going to Old Oak Common or Paddington/Euston).
At 500 passengers an hour (9,000 a day), assuming £15 a ticket over a year that's £48 million for 10 coach trains (well 8 coach trains but +2 coaches per train to allow for spares) just between Heathrow and Woking, that's enough to cover the likely running costs of the trains (assuming £200,000 per coach in lease costs and that's 1/3 of the total running costs).
Now, is likely that Woking to Heathrow at £15 for one way is very likely to be a too high (RailAir from Woking for a single is £11 and a return is the equivalent of £8.25 each way).
However, that's assuming an average of 125 people per train and not considering that you may find staff using it as well as passengers as well as other travel it generates.
If we were looking to set ticket prices at an average of £8 (so to undercut RailAir) from Woking and beyond, rather than 125 people per hour you'd need 230. However, that wouldn't even need to be all Heathrow based travel.
For example, 3 extra people travelling Fleet to Woking would reduce that count by 1.
Also, a passenger travelling from Farnborough to Old Oak Common with a ticket of (say) £16 would reduce that passenger count by 2.
Finally £8 is probably a little low for the average cost, as at Woking you only need to be an average of £8 to undercut RailAir's standard return, from Woking that might be £14 (£7 each way). For a standard off peak return to Woking from Guildford £4.90 whilst from Basingstoke it's £11.50, so for through ticketing (where most of those travelling would take the direct train rather than changing) to generate an average of £16 return, each leg could be £6 extra, or £17 return from Guildford and £23.50 from Basingstoke.
Given that petrol costs would be circa £25 return from Basingstoke to Heathrow those ticket prices would undercut driving for someone going on their own and with parking it could still be fairly good value for 3 or maybe even 4 people going if they were going for a longer holiday.
If prices were at that level, it would attract quite a lot of current travellers, even before you consider the uplift from the extra capacity for local travel.
If prices were higher then the number of passengers you'd need per train would reduce. Also, bear in mind that's on off peak prices, so peak prices would drag the average up a little.
Anyway 230 people on a train capable of carrying over 400 people, which would be busy people could get a pair of seats too themselves except those travelling together who may take a pair of seats or three out of four, as such it would be fairly busy, but not so much that any would have to stand (except at peak times, but then other trains would be much quieter)